Referring to FIG. 1, a representative implementation of a telephone network link 1 is illustrated. Hybrid circuit 2 connects a near-end user telephone 5 to the network 1 and hybrid circuit 9 connects a far-end user 11 to the network 1. Since the trunk 13 interconnecting the near-end central office 12 and the far-end central office 14 conveys digital communications, analog-to-digital (A/D) converters 3 and 10 connect the transmitter side of the hybrid circuits at each end of the network, to the digital trunk circuit 13. Similarly, digital-to-analog (D/A) converters 4 and 8 connect the receiver side of the hybrid circuit to the digital trunk circuit 13. Using this network structure, an end-to-end voice communication may take place between two end-user devices 5 and 11 of the telephone network.
Each hybrid circuit 2, 9 is a converter that interconnects a two-wire circuit of the telephone to a four-wire circuit of the central office 12, 14. Both the two-wire and four-wire circuits support the simultaneous communication of transmit and receive signals. However, the four-wire circuit of the Public Switched Telephone Network (PSTN) uses one wire pair for the transmit signal and the other wire pair for the receive signal, while the two-wire circuit must carry both the transmit and receive signals on a single wire pair. Because the transmit and receive signals are duplexed on the single wire pair, part of the transmitted signal energy 18 and/or 16 originating from the telephone 5 and/or 11 can be reflected back to the telephone by the hybrid circuits 9 and 2, respectively. This reflected energy, though delayed in time, substantially replicates the transmitted signal and causes undesirable interference. When the transmitted signal is human speech, the speaker may hear his or her own speech in the receiver as a delayed and attenuated echo.
For example, when a user speaks into telephone 5 the voice signal energy is transmitted to telephone 11 through hybrid 9. Echo is created when the transmitted signal is reflected back by the hybrid circuit 9 and passes through the PSTN to the originating telephone. This echo is annoying to the users of the communication link.
The quality of the communication link may be improved by subtracting a replica of the originally transmitted signal from the echo signal generated by the hybrid circuit at the far-end of the communication link. Since the signal transmitted by the hybrid circuit at the far end contains both the echo and the far-end user's voice signal of interest, subtracting the replica of the originally transmitted near-end signal from the transmitted far-end signal will reduce or eliminate the echo, and retain the far-end user's voice signal.
As illustrated in FIG. 1, signal splitter 15 provides the signal 18a to D/A 8 and to filter 19 which provides a negative replica −18 of the originally transmitted signal 18 to a combiner circuit 17 at the same time the combined echo signal 18′ and far-end signal of interest 16 is provided to the combiner circuit 17. The echo canceller circuit 7 contains amplification/attenuation circuitry that attempts to match the amplitude of the replica signal −18 with that of the echo signal 18′. By precisely matching the absolute values of the signal amplitudes of the negative replica −18 and the echo signal 18′, as they are provided to the combiner circuit 17, the echo may be removed entirely from the signal 16a received by the near-end user. However, the complete removal of the echo only occurs under ideal conditions. After being summed by the combiner 17, the sum of the signal energies is conveyed to the near-end telephone receiver as signal 16a. 
A real-world implementation of the communication link represented by FIG. 1 does not provide the ideal conditions needed to entirely eliminate the signal. The original signal information contained in the echo signal 18′, which is received by the combiner 17, is distorted by the non-linearities present in the A/D and D/A conversions that the original signal 18 has undergone.
The μ-law or A-law A/D and D/A conversions experienced within the transmission path are nonlinear in nature and present a significant problem to the linear adaptive filter 19 typically used in echo cancellers. Additional signal distortion is caused by the non-linearity of the hybrid circuit 9. The linear adaptive filter 19 cannot match the non-linear distortions introduced by the μ-law or A-law conversions and the hybrid circuit 9 and, as a result, cannot cancel them. Therefore, a typical voice communication link over the PSTN is subject to echo that cannot be completely cancelled using conventional approaches, such as linear adaptive filtering. In essence, the echo canceller synthesizes the estimated echo, which is subtracted from the composite signal (16, 18′) of the combined far-end signal of interest 16 and echo 18′. Together, the signal distortion caused by the non-linearities of the multiple conversions and the inability of the echo canceller to precisely model the true echo path limit the realizable echo rejection.